✦ LIBER ✦

On a problem of H. N. Gupta

✍ Scribed by Andreas Blass; Victor Pambuccian

Publisher: Springer
Year: 1996
Tongue: English
Weight: 127 KB
Volume: 61
Category: Article
ISSN: 0046-5755
DOI: 10.1007/bf00150031

No coin nor oath required. For personal study only.

✦ Synopsis

It is shown that the axiom 'For any points x, y, z such that y is between x and z, there is a right triangle having x and z as endpoints of the hypotenuse and y as foot of the altitude to the hypotenuse', when added to three-dimensional Euclidean geometry over arbitrary ordered fields, is weaker than the axiom 'Every line which passes through the interior of a sphere intersects that sphere'.

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